Astanding wave pattern is created on a string with mass density μ = 3.4 × 10-4 kg/m. a wave generator with frequency f = 61 hz is attached to one end of the string and the other end goes over a pulley and is connected to a mass (ignore the weight of the string between the pulley and mass). the distance between the generator and pulley is l = 0.62 m. initially the 3rd harmonic wave pattern is formed.
1) what is the wavelength of the wave? m 2) what is the speed of the wave? m/s 3) what is the tension in the string? n 4) what is the mass hanging on the end of the string? kg 5)now the hanging mass is adjusted to create the 2nd harmonic. the frequency is held fixed at f = 61 hz.what is the wavelength of the wave? m 6) what is the speed of the wave? m/s 7) what is the tension in the string? n 8) what is the mass hanging on the end of the string? kg 9) keeping the frequency fixed at f = 61 hz, what is the maximum mass that can be used to still create a coherent standing wave pattern?
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Ответ:
1) λ = 0.413 m , 2)v = 25,213 m / s , 3) T = 0.216 N , 4) m = 22.04 10-3 kg
Explanation:
1) The resonance occurs when the traveling wave bounces at the ends and the two waves are added, the ends as they are fixed have a node, the wavelength and the length of the string are related
λ = 2L / n n = 1, 2, 3 ...
In this case L = 0.62 m and n = 3
Let's calculate
λ = 2 0.62 / 3
λ = 0.413 m
2) the velocity related to wavelength and frequency
v = λ f
v = 0.413 61
v = 25,213 m / s
3) let's use the equation
v = √T /μ
T = v² μ
T = 25,213² 3.4 10⁻⁴
T = 0.216 N
4) the rope tension is proportional to the hanging weight
T-W = 0
T = W
W = m g
m = W / g
m = 0.216 / 9.8
m = 22.04 10-3 kg
5) n = 2
λ = 2 0.62 / 2
λ = 0.62 m
6) v = λ f
v = 0.62 61
v = 37.82 m / s
7) T = v² μ
T = 37.82² 3.4 10⁻⁴
T = 0.486 N
8) m = W / g
m = 0.486 / 9.8
m = 49.62 10⁻³ kg
9) n = 1
λ = 2 0.62
λ = 1.24 m
v = 1.24 61
v = 75.64 m / s
T = v² miu
T = 75.64² 3.4 10⁻⁴
T = 2.572 10⁻² N
m = 2.572 10⁻² / 9.8
m = 262.4 10⁻³ kg
Ответ:
Hence, the small beefs with fall out, and the large ones will remain in the sieve/net.